
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import plotly.express as px

%matplotlib inline

# Library needed for performing statistical tests
from scipy import stats

# Needed for normalisation
from sklearn import preprocessing
from sklearn import cluster, metrics
from sklearn.decomposition import PCA

# Libraries needed for training the clustering algorithms
from sklearn.cluster import KMeans
from sklearn.mixture import GaussianMixture as GMM
from sklearn.cluster import DBSCAN

# Import the silhouette_score function from sklearn.metrics
from sklearn.metrics import silhouette_score

# Library needed for social network graph
import networkx as nx

import warnings
warnings.filterwarnings('ignore')


# Load `metro.csv` into a dataframe `metro_bike` and displaying the first five rows.
metro_bike = pd.read_csv('metro.csv')
metro_bike.head()


# use `.describe()` to get numerical columns
metro_bike.describe()


metro_bike.shape

(92124, 15)


metro_bike.dtypes

trip_id                  int64
duration                 int64
start_time              object
end_time                object
start_station            int64
start_lat              float64
start_lon              float64
end_station              int64
end_lat                float64
end_lon                float64
bike_id                 object
plan_duration            int64
trip_route_category     object
passholder_type         object
bike_type               object
dtype: object


# Check for null/missing values to handle in data cleaning
metro_bike.isnull().sum()

trip_id                   0
duration                  0
start_time                0
end_time                  0
start_station             0
start_lat              2139
start_lon              2139
end_station               0
end_lat                4072
end_lon                4072
bike_id                   0
plan_duration             0
trip_route_category       0
passholder_type           0
bike_type                 0
dtype: int64


# Since `trip_id` is unique for all the values, we can set it to be the index.
metro_bike.set_index('trip_id', inplace=True)


metro_bike.head()


# `inplace` is added as a parameter to modify the current dataframe itself.
metro_bike.dropna(inplace=True)
metro_bike.isnull().sum()

duration               0
start_time             0
end_time               0
start_station          0
start_lat              0
start_lon              0
end_station            0
end_lat                0
end_lon                0
bike_id                0
plan_duration          0
trip_route_category    0
passholder_type        0
bike_type              0
dtype: int64


metro_bike.shape

(86760, 14)


# `.info` is used to find a brief overview of the non null rows and data type.
metro_bike.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 86760 entries, 124657107 to 130053088
Data columns (total 14 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   duration             86760 non-null  int64  
 1   start_time           86760 non-null  object 
 2   end_time             86760 non-null  object 
 3   start_station        86760 non-null  int64  
 4   start_lat            86760 non-null  float64
 5   start_lon            86760 non-null  float64
 6   end_station          86760 non-null  int64  
 7   end_lat              86760 non-null  float64
 8   end_lon              86760 non-null  float64
 9   bike_id              86760 non-null  object 
 10  plan_duration        86760 non-null  int64  
 11  trip_route_category  86760 non-null  object 
 12  passholder_type      86760 non-null  object 
 13  bike_type            86760 non-null  object 
dtypes: float64(4), int64(4), object(6)
memory usage: 9.9+ MB


metro_bike.duration.hist(bins=50, range=(1,45))

plt.xlabel("Minutes")
plt.ylabel("Frequency")

Text(0, 0.5, 'Frequency')


# Use .mean() and .median() for mean and median values
metro_bike.duration.mean(), metro_bike.duration.median()

(26.99640387275242, 11.0)


metro_bike.hist(figsize=(10, 10))

array([[<AxesSubplot:title={'center':'duration'}>,
        <AxesSubplot:title={'center':'start_station'}>,
        <AxesSubplot:title={'center':'start_lat'}>],
       [<AxesSubplot:title={'center':'start_lon'}>,
        <AxesSubplot:title={'center':'end_station'}>,
        <AxesSubplot:title={'center':'end_lat'}>],
       [<AxesSubplot:title={'center':'end_lon'}>,
        <AxesSubplot:title={'center':'plan_duration'}>, <AxesSubplot:>]],
      dtype=object)


metro_bike_new = metro_bike[metro_bike.duration < 360]
metro_bike_new.shape

(85974, 14)


metro_bike_new.duration.hist(bins=50, range=(1,90))

plt.xlabel("Minutes")
plt.ylabel("Frequency")

Text(0, 0.5, 'Frequency')


metro_bike['plan_duration'].value_counts()

30     55907
1      21451
365     9375
999       27
Name: plan_duration, dtype: int64


p_d = sns.countplot(x='plan_duration', data=metro_bike)
for p in p_d.patches:
    p_d.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
p_d.set(xlabel='Plan Duration', ylabel='Count')
p_d.set_title('Count of Plan Duration')

Text(0.5, 1.0, 'Count of Plan Duration')


metro_bike['trip_route_category'].value_counts()

One Way       72029
Round Trip    14731
Name: trip_route_category, dtype: int64


sns.set(rc={'figure.figsize':(11,9)})
trip_cat = sns.countplot(x='trip_route_category', data=metro_bike)
for p in trip_cat.patches:
    trip_cat.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
trip_cat.set(xlabel='Trip Route', ylabel='Count')
trip_cat.set_title('Count of various Trip Categories')

Text(0.5, 1.0, 'Count of various Trip Categories')


metro_bike['passholder_type'].value_counts()

Monthly Pass    55904
Walk-up         21258
Annual Pass      5966
One Day Pass     3599
Testing            27
Flex Pass           6
Name: passholder_type, dtype: int64


sns.set(rc={'figure.figsize':(11,7)})
pass_type = sns.countplot(x='passholder_type', data=metro_bike)
for p in pass_type.patches:
    pass_type.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
pass_type.set(xlabel='Types of Passes', ylabel='Count')
pass_type.set_title('Count of various Passes Available')

Text(0.5, 1.0, 'Count of various Passes Available')


metro_bike['bike_type'].value_counts()

electric    45818
standard    28966
smart       11976
Name: bike_type, dtype: int64


sns.set(rc={'figure.figsize':(11,8)})
bike_type = sns.countplot(x='bike_type', data=metro_bike)
for p in bike_type.patches:
    bike_type.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
bike_type.set(xlabel='Types of Bikes', ylabel='Count')
bike_type.set_title('Count of Various Bikes Available')

Text(0.5, 1.0, 'Count of Various Bikes Available')


pdf = sns.distplot(metro_bike['plan_duration'])
pdf.set(xlabel='Plan Duration', ylabel='Density')
pdf.set_title('Probability Density Function of Plan Duration')
plt.show()


metro_bike['start_time'] = pd.to_datetime(metro_bike['start_time'])
metro_bike['end_time'] = pd.to_datetime(metro_bike['end_time'])

metro_bike.head()


metro_bike.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 86760 entries, 124657107 to 130053088
Data columns (total 14 columns):
 #   Column               Non-Null Count  Dtype         
---  ------               --------------  -----         
 0   duration             86760 non-null  int64         
 1   start_time           86760 non-null  datetime64[ns]
 2   end_time             86760 non-null  datetime64[ns]
 3   start_station        86760 non-null  int64         
 4   start_lat            86760 non-null  float64       
 5   start_lon            86760 non-null  float64       
 6   end_station          86760 non-null  int64         
 7   end_lat              86760 non-null  float64       
 8   end_lon              86760 non-null  float64       
 9   bike_id              86760 non-null  object        
 10  plan_duration        86760 non-null  int64         
 11  trip_route_category  86760 non-null  object        
 12  passholder_type      86760 non-null  object        
 13  bike_type            86760 non-null  object        
dtypes: datetime64[ns](2), float64(4), int64(4), object(4)
memory usage: 11.9+ MB


metro_bike['start_day'] = metro_bike['start_time'].dt.dayofweek

days_of_week = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']

metro_bike['start_month'] = metro_bike['start_time'].dt.month_name()
metro_bike['start_hour'] = metro_bike['start_time'].dt.hour
metro_bike['start_date'] = metro_bike['start_time'].dt.date
metro_bike['starting_time'] = metro_bike['start_time'].dt.time
metro_bike['end_hour'] = metro_bike['end_time'].dt.hour

metro_bike.head()


metro_bike.groupby('start_day').count()['bike_type'].plot(figsize=(12,8))
plt.xlabel("Days of the Week")
plt.ylabel("Frequency of the Bikes rented")
plt.title("Daily Bike Frequency")
plt.show()


count_day = sns.countplot(x='start_day', data=metro_bike)
for p in count_day.patches:
    count_day.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
count_day.set(xlabel='Day of the Week', ylabel='Count')
count_day.set_title('Count of Bikes based on Days')

Text(0.5, 1.0, 'Count of Bikes based on Days')


# Plot bike ride for each hour of the day for the entire week
plt.figure(figsize=(24,8))

# Plot the countplot with a legend to the side
sns.countplot(x='start_day', hue='start_hour', data=metro_bike, palette='terrain')
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5), ncol=2)

<matplotlib.legend.Legend at 0x7f98569b30d0>


# Create a sunburst plot using the 'start_hour' and 'start_station' columns
fig = px.sunburst(metro_bike, path=['start_hour', 'start_station'], color='start_hour')

fig.update_layout(title='Start Hour vs Start Station')
fig.show()


# Create a sunburst plot using the 'end_hour' and 'end_station' columns
fig = px.sunburst(metro_bike, path=['end_hour', 'end_station'], color='end_station')

fig.update_layout(title='End hour vs End Station')
fig.show()


# Group the data by hour and day of the week and compute the mean duration
mean_duration = metro_bike.groupby(['start_hour', 'start_day'])['duration'].mean().reset_index()

# Loop over the days of the week
for day in range(7):
    # Select the data for the current day
    data = mean_duration[mean_duration['start_day'] == day]
    
    # Create a barplot
    duration_plot = sns.barplot(x='start_hour', y='duration', data=data, palette='RdYlBu')
    
    duration_plot.set(xlabel='Start Hour', ylabel='Duration')
    
    # Set the title of the plot
    duration_plot.set_title(days_of_week[day])
    
    # Show the plot
    plt.show()


mean_duration1 = metro_bike.groupby(['start_hour'])['duration'].mean().reset_index()

dur_hour = sns.lineplot(x='start_hour', y='duration', data=mean_duration1)
for line in range(0, mean_duration1.shape[0]):
    dur_hour.text(mean_duration1.start_hour[line], mean_duration1.duration[line], round(mean_duration1.duration[line], 1), 
            horizontalalignment='left', size='medium', color='grey', weight='semibold')
dur_hour.set(xlabel='Start Hour', ylabel='Mean Duration')
dur_hour.set_title('Mean Duration vs Starting Hour')

Text(0.5, 1.0, 'Mean Duration vs Starting Hour')


mean_duration2 = metro_bike.groupby(['start_day'])['duration'].mean().reset_index()

dur_day = sns.lineplot(x='start_day', y='duration', data=mean_duration2)
for line in range(0, mean_duration2.shape[0]):
    dur_day.text(mean_duration2.start_day[line], mean_duration2.duration[line], round(mean_duration2.duration[line], 1), 
            horizontalalignment='left', size='medium', color='green', weight='semibold')
dur_day.set(xlabel='Day of the Week', ylabel='Mean Duration')
dur_day.set_title('Mean Duration vs Day of the Week')

Text(0.5, 1.0, 'Mean Duration vs Day of the Week')


metro_bike['start_month'].value_counts()

August       30876
September    28716
July         27168
Name: start_month, dtype: int64


sns.set(rc={'figure.figsize':(11,8)})
month_count = sns.countplot(x='start_month', data=metro_bike)
for p in month_count.patches:
    month_count.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
month_count.set(xlabel='Month', ylabel='Count')
month_count.set_title('Count of Bikes rented based on Month')

Text(0.5, 1.0, 'Count of Bikes rented based on Month')


labels = ['August','September','July']
plt.pie(x=metro_bike.groupby('start_month').count()['duration'].sort_values(ascending=False), 
        autopct='%1.1f%%',labels = labels)
plt.title("Percentile Distribution per Month")
plt.show()


hour_count = sns.countplot(x='start_hour', data=metro_bike)
for p in hour_count.patches:
    hour_count.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
hour_count.set(xlabel='Hour', ylabel='Count')
hour_count.set_title('Count of Bikes rented based on Hour of the Day')

Text(0.5, 1.0, 'Count of Bikes rented based on Hour of the Day')


# Create a cross-tabulation of the 'passholder_type' and 'bike_type' columns
pass_bike = pd.crosstab(metro_bike['passholder_type'], metro_bike['bike_type'])

# Plot the cross-tabulation as a bar plot
ax = pass_bike.plot(kind='bar', figsize=(15, 15))

for p in ax.patches:
    ax.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')

plt.xlabel('Passholder Type')
plt.ylabel('Count')
plt.title('Passholder Type over various Bike Types')

Text(0.5, 1.0, 'Passholder Type over various Bike Types')


mean_duration3 = metro_bike.groupby('bike_type')['duration'].mean().reset_index()

dur_bike = sns.barplot(x='bike_type', y='duration', data=mean_duration3, color='red', palette='pastel')
for p in dur_bike.patches:
    dur_bike.text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
dur_bike.set(xlabel='Bike Type', ylabel='Duration')
dur_bike.set_title('Mean Duration of Various Bike Types')

Text(0.5, 1.0, 'Mean Duration of Various Bike Types')


metro_by_passholder = metro_bike.groupby("passholder_type")

duration_by_passholder = metro_by_passholder["duration"]

mean_duration_by_passholder = duration_by_passholder.mean()

# Create a figure with multiple subplots
fig, axs = plt.subplots(nrows=len(mean_duration_by_passholder.index)-1, ncols=1, 
                        figsize=(20, 6*len(mean_duration_by_passholder.index)))

# Loop through each pair of passholder types and plot the t-statistic values
for i, passholder_type1 in enumerate(mean_duration_by_passholder.index[:-1]):
  for j, passholder_type2 in enumerate(mean_duration_by_passholder.index[i+1:]):
    t_stat, p_value = stats.ttest_ind(duration_by_passholder.get_group(passholder_type1), 
                                      duration_by_passholder.get_group(passholder_type2))
    print(f'{passholder_type1} vs. {passholder_type2}: p-value = {p_value}')
    axs[i].bar(f"{passholder_type1} vs. {passholder_type2}", p_value)
    axs[i].set_title(f"p-value for {passholder_type1}")
    for p in axs[i].patches:
        axs[i].text(p.get_x() + p.get_width()/2, p.get_height(), p.get_height(), ha='center')
    axs[i].set_xlabel("Passholder types")
    axs[i].set_ylabel("p-value")

plt.show()

Annual Pass vs. Flex Pass: p-value = 0.8158212864252368
Annual Pass vs. Monthly Pass: p-value = 0.0031987234897233076
Annual Pass vs. One Day Pass: p-value = 8.288939500446688e-155
Annual Pass vs. Testing: p-value = 0.2395399041543238
Annual Pass vs. Walk-up: p-value = 7.970594234589781e-87
Flex Pass vs. Monthly Pass: p-value = 0.6891909679056905
Flex Pass vs. One Day Pass: p-value = 0.30731294748527543
Flex Pass vs. Testing: p-value = 0.4103221827358773
Flex Pass vs. Walk-up: p-value = 0.46382909975284303
Monthly Pass vs. One Day Pass: p-value = 0.0
Monthly Pass vs. Testing: p-value = 0.19523283057602708
Monthly Pass vs. Walk-up: p-value = 0.0
One Day Pass vs. Testing: p-value = 0.11446433041037984
One Day Pass vs. Walk-up: p-value = 3.814834116252384e-19
Testing vs. Walk-up: p-value = 0.3668698793884352


# Load the dataset `seeds.csv` into a dataframe `seeds`
seeds = pd.read_csv('seeds.csv')
seeds.head()


seeds.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 210 entries, 0 to 209
Data columns (total 7 columns):
 #   Column         Non-Null Count  Dtype  
---  ------         --------------  -----  
 0   area           210 non-null    float64
 1   perimeter      210 non-null    float64
 2   compactness    210 non-null    float64
 3   length         210 non-null    float64
 4   width          210 non-null    float64
 5   asymmetry      210 non-null    float64
 6   groove_length  210 non-null    float64
dtypes: float64(7)
memory usage: 11.6 KB


seeds.describe()


seeds.isna().sum()

area             0
perimeter        0
compactness      0
length           0
width            0
asymmetry        0
groove_length    0
dtype: int64


seeds.duplicated().sum()

0


pair_plot = sns.pairplot(seeds, hue='perimeter')
pair_plot.fig.suptitle('Plot of Seeds Data', y=1.03)

Text(0.5, 1.03, 'Plot of Seeds Data')


corr_matrix = seeds.corr()
sns.set(rc={'figure.figsize':(12,10)})
sns.heatmap(corr_matrix, vmax=1, square=True, cmap='RdYlGn')

<AxesSubplot:>


seeds.shape

(210, 7)


# Perform PCA to find two principal components before clustering for improving performance of the algorithms
pca = PCA(n_components=2)
seeds_pca = pca.fit_transform(seeds)


seeds_pca_df = pd.DataFrame(seeds_pca, columns=['col1', 'col2'])


pca_plot = sns.pairplot(seeds_pca_df);
pca_plot.fig.suptitle('Plot of Seeds PCA Data', y=1.03)

Text(0.5, 1.03, 'Plot of Seeds PCA Data')


# Create an empty list to store the silhouette scores
silhouette_scores = []

# Loop through the number of clusters to use for k-means
for n in range(2, 8):
    # Perform k-means clustering on the PCA data
    kmeans = KMeans(n_clusters=n)
    seeds_pca_df[f'{n}_clusters'] = kmeans.fit_predict(seeds_pca_df)
    
    # Calculate the silhouette score for the current number of clusters
    score = silhouette_score(seeds_pca_df, seeds_pca_df[f'{n}_clusters'])
    
    # Append the silhouette score to the list
    silhouette_scores.append(score)

# Create a figure with 3 rows and 3 columns of subplots
fig, ax = plt.subplots(3, 2, sharex=True, sharey=True, figsize=(10, 8))

# Loop through each row and column in the figure
for row in range(3):
    for col in range(2):
        # Set the color palette for the current subplot
        n_clusters = 3*col + row + 2
        color_map = plt.cm.get_cmap('inferno', n_clusters)
        
        # Create a scatterplot on the current subplot using the 'PCA1' and 'PCA2' columns as the x and y values, respectively
        ax[row, col].scatter(seeds_pca_df['col1'], seeds_pca_df['col2'], 
                             c=seeds_pca_df[f'{n_clusters}_clusters'], cmap=color_map)
        
        # Set the title of the current subplot
        ax[row, col].set_title(f"{n_clusters} Clusters\nSilhouette Score = {silhouette_scores[n_clusters-2]:.3f}")
        
        # Add a grid to the current subplot
        ax[row, col].grid(True)

# Add a title to the figure
plt.suptitle("KMeans Clustering")

# Tighten the layout of the figure
fig.tight_layout()


# Arbitrarily selecting a range of values for K to perfrom elbow method
K = range(1,11)
sum_of_squared_distances = []
# Using Scikit Learn’s KMeans Algorithm to find sum of squared distances
for k in K:
    model = KMeans(n_clusters=k).fit(seeds_pca_df)
    sum_of_squared_distances.append(model.inertia_)
plt.plot(K, sum_of_squared_distances)
plt.xlabel('K values')
plt.ylabel('Sum of Squared Distances')
plt.title('Elbow Method')
plt.show()


# Initialize lists to store the silhouette scores and WCSS
silhouette_scores = []

for p in range(2, 8):
    # Perform GMM clustering on the PCA data
    gmm = GMM(n_components=p)
    seeds_pca_df[f'{p}_clusters'] = gmm.fit_predict(seeds_pca_df)
    
    # Compute the silhouette score for the current clustering model
    silhouette_scores.append(silhouette_score(seeds_pca_df, seeds_pca_df[f'{p}_clusters']))

# Create a figure with 3 rows and 3 columns of subplots
fig, ax = plt.subplots(3, 2, sharex=True, sharey=True, figsize=(10, 8))

# Loop through each row and column in the figure
for row in range(3):
    for col in range(2):
        # Set the color palette for the current subplot
        n_clusters = 3*col + row + 2
        color_map = plt.cm.get_cmap('magma', n_clusters)
        
        # Create a scatterplot on the current subplot using the 'PCA1' and 'PCA2' columns as the x and y values, respectively
        ax[row, col].scatter(seeds_pca_df['col1'], seeds_pca_df['col2'], 
                             c=seeds_pca_df[f'{n_clusters}_clusters'], cmap=color_map)
        
        # Set the title of the current subplot
        ax[row, col].set_title(f"{n_clusters} Clusters\nSilhouette Score = {silhouette_scores[n_clusters-2]:.3f}")
        
        # Add a grid to the current subplot
        ax[row, col].grid(True)

# Add a title to the figure
plt.suptitle("GMM Clustering")

# Tighten the layout of the figure
fig.tight_layout()


eps = 1.0
min_samples = 10

# Initialise and fit DBSCAN
db = DBSCAN(eps=eps, min_samples=min_samples).fit(seeds_pca_df)
labels = db.labels_

plt.scatter(seeds_pca_df['col1'], seeds_pca_df['col2'], s=15, c=labels, cmap='jet')
plt.title(f'DBSCAN, eps={eps}, min_samples={min_samples}, n_clusters={max(labels)+2}')
plt.gca().set_aspect('equal')


# No column names in the dataset, so we add them
colnames=['nodes', 'edges']


# Load the dataset `social-network.csv` into `soc_net`
soc_net = pd.read_csv('social-network.csv', names=colnames, header=None)
soc_net.head()


soc_net.describe()


soc_net.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2981 entries, 0 to 2980
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype
---  ------  --------------  -----
 0   nodes   2981 non-null   int64
 1   edges   2981 non-null   int64
dtypes: int64(2)
memory usage: 46.7 KB


# The function `nx.from_pandas_edgelist()` takes `nodes` and `edges` as parameters.
net_graph = nx.from_pandas_edgelist(soc_net, source='nodes', target='edges')
net_graph

<networkx.classes.graph.Graph at 0x7f9862080430>


net_graph.number_of_nodes()

2888


net_graph.number_of_edges()

2981


net_graph.nodes()

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(710, 2529), (710, 2530), (710, 2531), (710, 2532), (710, 2533), (710, 2534), (710, 2535), (714, 711), (714, 716), (714, 719), (714, 720), (714, 721), (714, 722), (714, 2348), (714, 2351), (714, 2352), (714, 2354), (714, 2356), (714, 2366), (714, 2369), (714, 2370), (714, 2375), (714, 2386), (714, 2394), (714, 2395), (714, 2399), (714, 2402), (714, 2405), (714, 2407), (714, 2409), (714, 2431), (714, 2434), (714, 2444), (714, 2452), (714, 2461), (714, 2465), (714, 2469), (714, 2475), (714, 2482), (714, 2483), (714, 2484), (714, 2492), (714, 2509), (714, 2511), (714, 2518), (714, 2521), (714, 2523), (714, 2524), (714, 2526), (714, 2530), (714, 2594), (714, 2595), (714, 2596), (714, 2597), (714, 2598), (714, 2599), (714, 2600), (714, 2601), (714, 2602), (714, 2603), (714, 2604), (714, 2605), (714, 2606), (714, 2607), (714, 2608), (714, 2609), (714, 2610), (714, 2611), (714, 2612), (714, 2613), (714, 2614), (714, 2615), (714, 2616), (714, 2617), (714, 2618), (714, 2619), (714, 2620), (714, 2621), (714, 2622), (714, 2623), (714, 2624), (714, 2625), (714, 2626), (714, 2627), (714, 2628), (714, 2629), (714, 2630), (714, 2631), (714, 2632), (714, 2633), (714, 2634), (714, 2635), (714, 2636), (714, 2637), (714, 2638), (714, 2639), (714, 2640), (714, 2641), (714, 2642), (714, 2643), (714, 2644), (714, 2645), (714, 2646), (714, 2647), (714, 2648), (714, 2649), (714, 2650), (714, 2651), (714, 2652), (714, 2653), (714, 2654), (714, 2655), (714, 2656), (714, 2657), (714, 2658), (714, 2659), (714, 2660), (714, 2661), (714, 2662), (714, 2663), (714, 2664), (714, 2665), (714, 2666), (714, 2667), (714, 2668), (714, 2669), (714, 2670), (714, 2671), (714, 2672), (714, 2673), (714, 2674), (714, 2675), (714, 2676), (714, 2677), (714, 2678), (714, 2679), (714, 2680), (714, 2681), (714, 2682), (714, 2683), (714, 2684), (714, 2685), (714, 2686), (335, 2232), (2232, 2233), (2232, 2234), (2232, 2235), (2232, 2236), (2232, 2237), (2232, 2238), (2232, 2239), (2232, 2240), (2232, 2241), (2232, 2242), (2232, 2243), (2232, 2244), (2232, 2245), (2232, 2246), (2232, 2247), (2232, 2248), (2232, 2249), (2232, 2250), (2232, 2251), (2232, 2252), (2232, 2253), (2232, 2254), (2232, 2255), (2232, 2256), (2232, 2257), (2232, 2258), (2232, 2259), (2232, 2260), (2232, 2261), (2232, 2262), (2232, 2263), (2232, 2264), (2232, 2265), (2232, 2266), (2232, 2267), (2232, 2268), (2232, 2269), (2232, 2270), (2232, 2271), (2232, 2272), (2232, 2273), (2232, 2274), (2232, 2275), (2232, 2276), (2232, 2277), (2232, 2278), (2232, 2279), (2232, 2280), (2232, 2281), (2232, 2282), (2232, 2283), (2232, 2284), (2232, 2285), (2232, 2286), (2232, 2287), (2232, 2288), (2232, 2289), (2232, 2290), (2232, 2291), (2232, 2292), (2232, 2293), (2232, 2294), (2232, 2295), (2232, 2296), (2232, 2297), (2232, 2298), (2232, 2299), (2232, 2300), (2232, 2301), (2232, 2302), (2232, 2303), (2232, 2304), (2232, 2305), (2232, 2306), (2232, 2307), (2232, 2308), (2232, 2309), (2232, 2310), (2232, 2311), (2232, 2312), (2232, 2313), (2232, 2314), (2232, 2315), (2232, 2316), (2232, 2317), (2232, 2318), (2232, 2319), (2232, 2320), (2232, 2321), (2232, 2322), (2232, 2323), (2232, 2324), (2232, 2325), (2232, 2326), (2232, 2327), (2232, 2328), (1524, 2699), (2594, 2536), (2699, 2687), (2699, 2698), (2699, 2709), (2699, 2714), (2699, 2720), (2699, 2730), (2699, 2746), (2699, 2748), (2699, 2754), (2699, 2773), (2699, 2775), (2699, 2777), (2699, 2801), (2699, 2804), (2699, 2805), (2699, 2806), (2699, 2811), (2699, 2824), (2699, 2826), (2699, 2829), (2699, 2831), (2699, 2841), (2699, 2857), (2699, 2858), (2699, 2859), (2699, 2860), (2699, 2861), (2699, 2862), (2699, 2863), (2699, 2864), (2699, 2865), (2699, 2866), (2699, 2867), (2699, 2868), (2699, 2869), (2699, 2870), (2699, 2871), (2699, 2872), (2699, 2873), (2699, 2874), (2699, 2875), (2699, 2876), (2699, 2877), (2699, 2878), (2699, 2879), (2699, 2880), (2699, 2881), (2699, 2882), (2699, 2883), (2699, 2884), (2699, 2885), (2699, 2886), (2699, 2887), (2699, 2888), (2536, 2537), (2536, 2538), (2536, 2539), (2536, 2540), (2536, 2541), (2536, 2542), (2536, 2543), (2536, 2544), (2536, 2545), (2536, 2546), (2536, 2547), (2536, 2548), (2536, 2549), (2536, 2550), (2536, 2551), (2536, 2552), (2536, 2553), (2536, 2554), (2536, 2555), (2536, 2556), (2536, 2557), (2536, 2558), (2536, 2559), (2536, 2560), (2536, 2561), (2536, 2562), (2536, 2563), (2536, 2564), (2536, 2565), (2536, 2566), (2536, 2567), (2536, 2568), (2536, 2569), (2536, 2570), (2536, 2571), (2536, 2572), (2536, 2573), (2536, 2574), (2536, 2575), (2536, 2576), (2536, 2577), (2536, 2578), (2536, 2579), (2536, 2580), (2536, 2581), (2536, 2582), (2536, 2583), (2536, 2584), (2536, 2585), (2536, 2586), (2536, 2587), (2536, 2588), (2536, 2589), (2536, 2590), (2536, 2591), (2536, 2592), (2536, 2593), (2687, 2688), (2687, 2689), (2687, 2690), (2687, 2691), (2687, 2692), (2687, 2693), (2687, 2694), (2687, 2695), (2687, 2696), (2687, 2697), (2687, 2698), (2687, 2700), (2687, 2701), (2687, 2702), (2687, 2703), (2687, 2704), (2687, 2705), (2687, 2706), (2687, 2707), (2687, 2708), (2687, 2709), (2687, 2710), (2687, 2711), (2687, 2712), (2687, 2713), (2687, 2714), (2687, 2715), (2687, 2716), (2687, 2717), (2687, 2718), (2687, 2719), (2687, 2720), (2687, 2721), (2687, 2722), (2687, 2723), (2687, 2724), (2687, 2725), (2687, 2726), (2687, 2727), (2687, 2728), (2687, 2729), (2687, 2730), (2687, 2731), (2687, 2732), (2687, 2733), (2687, 2734), (2687, 2735), (2687, 2736), (2687, 2737), (2687, 2738), (2687, 2739), (2687, 2740), (2687, 2741), (2687, 2742), (2687, 2743), (2687, 2744), (2687, 2745), (2687, 2746), (2687, 2747), (2687, 2748), (2687, 2749), (2687, 2750), (2687, 2751), (2687, 2752), (2687, 2753), (2687, 2754), (2687, 2755), (2687, 2756), (2687, 2757), (2687, 2758), (2687, 2759), (2687, 2760), (2687, 2761), (2687, 2762), (2687, 2763), (2687, 2764), (2687, 2765), (2687, 2766), (2687, 2767), (2687, 2768), (2687, 2769), (2687, 2770), (2687, 2771), (2687, 2772), (2687, 2773), (2687, 2774), (2687, 2775), (2687, 2776), (2687, 2777), (2687, 2778), (2687, 2779), (2687, 2780), (2687, 2781), (2687, 2782), (2687, 2783), (2687, 2784), (2687, 2785), (2687, 2786), (2687, 2787), (2687, 2788), (2687, 2789), (2687, 2790), (2687, 2791), (2687, 2792), (2687, 2793), (2687, 2794), (2687, 2795), (2687, 2796), (2687, 2797), (2687, 2798), (2687, 2799), (2687, 2800), (2687, 2801), (2687, 2802), (2687, 2803), (2687, 2804), (2687, 2805), (2687, 2806), (2687, 2807), (2687, 2808), (2687, 2809), (2687, 2810), (2687, 2811), (2687, 2812), (2687, 2813), (2687, 2814), (2687, 2815), (2687, 2816), (2687, 2817), (2687, 2818), (2687, 2819), (2687, 2820), (2687, 2821), (2687, 2822), (2687, 2823), (2687, 2824), (2687, 2825), (2687, 2826), (2687, 2827), (2687, 2828), (2687, 2829), (2687, 2830), (2687, 2831), (2687, 2832), (2687, 2833), (2687, 2834), (2687, 2835), (2687, 2836), (2687, 2837), (2687, 2838), (2687, 2839), (2687, 2840), (2687, 2841), (2687, 2842), (2687, 2843), (2687, 2844), (2687, 2845), (2687, 2846), (2687, 2847), (2687, 2848), (2687, 2849), (2687, 2850), (2687, 2851), (2687, 2852), (2687, 2853), (2687, 2854), (2687, 2855), (2687, 2856), (2687, 2857)])


# Use `nx.draw_networkx` to visualise graphs
plt.figure(figsize=(10,8))
nx.draw_networkx(net_graph)


# Visualise just the nodes
nx.draw_networkx_nodes(net_graph, pos=nx.spring_layout(net_graph))

<matplotlib.collections.PathCollection at 0x7f986067aaf0>


# Visualise just the edges
nx.draw_networkx_edges(net_graph, pos=nx.kamada_kawai_layout(net_graph))

<matplotlib.collections.LineCollection at 0x7f985988ea60>


G=net_graph
layout = nx.spring_layout(G)
plt.title('Spring Layout of Social Network Graph')
nx.draw(G,pos=layout,node_size=150,alpha=0.5)


G=net_graph
layout = nx.spectral_layout(G)
plt.title('Spectral Layout of Social Network Graph')
nx.draw(G,pos=layout,node_size=150,alpha=0.5)


nx.degree(net_graph, 1525)

710


nx.degree(net_graph, 603)

769


nx.degree(net_graph, 288)

481


nx.number_connected_components(net_graph)

1


nx.diameter(net_graph)

9


nx.density(net_graph)

0.0007150690793671507


nx.shortest_path(net_graph, 1, 2720)

[1, 69, 603, 1524, 2699, 2720]


# Source: https://networkx.org/nx-guides/content/exploratory_notebooks/facebook_notebook.html#centrality-measures

degree_centrality = nx.centrality.degree_centrality(net_graph)
(sorted(degree_centrality.items(), key=lambda item: item[1], reverse=True))[:10]

[(603, 0.2663664703844822),
 (1525, 0.24593003117422932),
 (288, 0.16660893661240042),
 (1, 0.09941115344648424),
 (710, 0.07655005195704884),
 (2687, 0.05888465535157603),
 (714, 0.04814686525805335),
 (2232, 0.03359889158295809),
 (2536, 0.020090058884655353),
 (2699, 0.019050917907862834)]


# Source: https://networkx.org/nx-guides/content/exploratory_notebooks/facebook_notebook.html#centrality-measures
(sorted(net_graph.degree, key=lambda item: item[1], reverse=True))[:10]

[(603, 769),
 (1525, 710),
 (288, 481),
 (1, 287),
 (710, 221),
 (2687, 170),
 (714, 139),
 (2232, 97),
 (2536, 58),
 (2699, 55)]


plt.figure(figsize=(8, 5))
plt.hist(degree_centrality.values(), bins=25)
plt.xticks(ticks=[0, 0.05, 0.1, 0.15, 0.2, 0.25])
plt.title("Degree Centrality Histogram ", fontdict={"size": 15}, loc="center")
plt.xlabel("Degree Centrality", fontdict={"size": 10})
plt.ylabel("Counts", fontdict={"size": 10})

Text(0, 0.5, 'Counts')


pos = pos = nx.spring_layout(net_graph)
node_size = [v * 1000 for v in degree_centrality.values()] 
plt.figure(figsize=(15, 8))
nx.draw_networkx(net_graph, pos=pos, node_size=node_size, with_labels=False, width=0.15)
plt.axis("off")

(-0.6573494791984558,
 1.060746443271637,
 -1.0745257794857026,
 0.5650426805019378)


# Use the function `.degree_histogram()`. 
# We skip the nodes that have a degree 0 
ddist = nx.degree_histogram(net_graph)[1:]
plt.loglog(range(1,len(ddist)+1),ddist,'o')

plt.title('Degree Distribution')
plt.xlabel('Degree')
plt.ylabel('Frequency')

Text(0, 0.5, 'Frequency')


ccg = nx.clustering(net_graph)
plt.hist(list(ccg.values()),bins='auto')
plt.title('Clustering Coefficient')
plt.xlabel("Clustering Coefficient")
plt.ylabel("Frequency")

Text(0, 0.5, 'Frequency')


betweenness_centrality = nx.betweenness_centrality(net_graph)
(sorted(betweenness_centrality.items(), key=lambda item: item[1], reverse=True))[:10]

[(603, 0.5497065448918781),
 (288, 0.46612992918844975),
 (1525, 0.4294450041419194),
 (247, 0.24124220674273653),
 (1, 0.1860965105682874),
 (2699, 0.13099957488596214),
 (1524, 0.13019147414713747),
 (710, 0.12724689931998354),
 (714, 0.11276804568283787),
 (2687, 0.09928765193746143)]


# Source: https://networkx.org/nx-guides/content/exploratory_notebooks/facebook_notebook.html#centrality-measures

plt.figure(figsize=(15, 8))
plt.hist(betweenness_centrality.values(), bins=100)
plt.xticks(ticks=[0, 0.062, 0.1, 0.128, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7])
plt.title("Betweenness Centrality Histogram ", fontdict={"size": 35}, loc="center")
plt.xlabel("Betweenness Centrality", fontdict={"size": 20})
plt.ylabel("Counts", fontdict={"size": 20})

Text(0, 0.5, 'Counts')


# Source: https://networkx.org/nx-guides/content/exploratory_notebooks/facebook_notebook.html#centrality-measures

pos = pos = nx.spring_layout(net_graph)
node_size = [v * 1000 for v in betweenness_centrality.values()]
plt.figure(figsize=(15, 8))
nx.draw_networkx(net_graph, pos=pos, node_size=node_size, with_labels=False, width=0.15)
plt.axis("off")

(-1.0439851224422454,
 0.728183263540268,
 -1.0939665377140044,
 0.9732972919940949)


nx.degree_assortativity_coefficient(net_graph)

-0.6682140067239861

	trip_id	duration	start_time	end_time	start_station	start_lat	start_lon	end_station	end_lat	end_lon	bike_id	plan_duration	trip_route_category	passholder_type	bike_type
0	124657107	5	7/1/2019 0:04	7/1/2019 0:09	4312	34.066990	-118.290878	4410	34.063351	-118.296799	6168	30	One Way	Monthly Pass	standard
1	124657587	9	7/1/2019 0:07	7/1/2019 0:16	3066	34.063389	-118.236160	3066	34.063389	-118.236160	17584	30	Round Trip	Monthly Pass	electric
2	124658068	5	7/1/2019 0:20	7/1/2019 0:25	4410	34.063351	-118.296799	4312	34.066990	-118.290878	18920	30	One Way	Monthly Pass	electric
3	124659747	20	7/1/2019 0:44	7/1/2019 1:04	3045	34.028511	-118.256668	4275	34.012520	-118.285896	6016	1	One Way	Walk-up	standard
4	124660227	27	7/1/2019 0:44	7/1/2019 1:11	3035	34.048401	-118.260948	3049	34.056969	-118.253593	5867	30	One Way	Monthly Pass	standard

	trip_id	duration	start_station	start_lat	start_lon	end_station	end_lat	end_lon	plan_duration
count	9.212400e+04	92124.000000	92124.000000	89985.000000	89985.000000	92124.000000	88052.000000	88052.000000	92124.000000
mean	1.274286e+08	33.168588	3484.899690	34.034786	-118.287893	3480.271026	34.034895	-118.286699	60.290977
std	1.524134e+06	129.057841	611.483883	0.058803	0.073501	609.942741	0.058790	0.072628	111.141364
min	1.246571e+08	1.000000	3000.000000	33.710979	-118.495422	3000.000000	33.710979	-118.495422	1.000000
25%	1.261375e+08	6.000000	3029.000000	34.035801	-118.281181	3028.000000	34.037048	-118.280952	1.000000
50%	1.274911e+08	12.000000	3062.000000	34.046810	-118.258537	3062.000000	34.046810	-118.258537	30.000000
75%	1.287379e+08	22.000000	4285.000000	34.051941	-118.248253	4285.000000	34.051941	-118.248253	30.000000
max	1.303877e+08	1440.000000	4453.000000	34.177662	-118.231277	4453.000000	34.177662	-118.231277	999.000000

	duration	start_time	end_time	start_station	start_lat	start_lon	end_station	end_lat	end_lon	bike_id	plan_duration	trip_route_category	passholder_type	bike_type
trip_id
124657107	5	7/1/2019 0:04	7/1/2019 0:09	4312	34.066990	-118.290878	4410	34.063351	-118.296799	6168	30	One Way	Monthly Pass	standard
124657587	9	7/1/2019 0:07	7/1/2019 0:16	3066	34.063389	-118.236160	3066	34.063389	-118.236160	17584	30	Round Trip	Monthly Pass	electric
124658068	5	7/1/2019 0:20	7/1/2019 0:25	4410	34.063351	-118.296799	4312	34.066990	-118.290878	18920	30	One Way	Monthly Pass	electric
124659747	20	7/1/2019 0:44	7/1/2019 1:04	3045	34.028511	-118.256668	4275	34.012520	-118.285896	6016	1	One Way	Walk-up	standard
124660227	27	7/1/2019 0:44	7/1/2019 1:11	3035	34.048401	-118.260948	3049	34.056969	-118.253593	5867	30	One Way	Monthly Pass	standard

	duration	start_time	end_time	start_station	start_lat	start_lon	end_station	end_lat	end_lon	bike_id	plan_duration	trip_route_category	passholder_type	bike_type
trip_id
124657107	5	2019-07-01 00:04:00	2019-07-01 00:09:00	4312	34.066990	-118.290878	4410	34.063351	-118.296799	6168	30	One Way	Monthly Pass	standard
124657587	9	2019-07-01 00:07:00	2019-07-01 00:16:00	3066	34.063389	-118.236160	3066	34.063389	-118.236160	17584	30	Round Trip	Monthly Pass	electric
124658068	5	2019-07-01 00:20:00	2019-07-01 00:25:00	4410	34.063351	-118.296799	4312	34.066990	-118.290878	18920	30	One Way	Monthly Pass	electric
124659747	20	2019-07-01 00:44:00	2019-07-01 01:04:00	3045	34.028511	-118.256668	4275	34.012520	-118.285896	6016	1	One Way	Walk-up	standard
124660227	27	2019-07-01 00:44:00	2019-07-01 01:11:00	3035	34.048401	-118.260948	3049	34.056969	-118.253593	5867	30	One Way	Monthly Pass	standard

	duration	start_time	end_time	start_station	start_lat	start_lon	end_station	end_lat	end_lon	bike_id	plan_duration	trip_route_category	passholder_type	bike_type	start_day	start_month	start_hour	start_date	starting_time	end_hour
trip_id
124657107	5	2019-07-01 00:04:00	2019-07-01 00:09:00	4312	34.066990	-118.290878	4410	34.063351	-118.296799	6168	30	One Way	Monthly Pass	standard	0	July	0	2019-07-01	00:04:00	0
124657587	9	2019-07-01 00:07:00	2019-07-01 00:16:00	3066	34.063389	-118.236160	3066	34.063389	-118.236160	17584	30	Round Trip	Monthly Pass	electric	0	July	0	2019-07-01	00:07:00	0
124658068	5	2019-07-01 00:20:00	2019-07-01 00:25:00	4410	34.063351	-118.296799	4312	34.066990	-118.290878	18920	30	One Way	Monthly Pass	electric	0	July	0	2019-07-01	00:20:00	0
124659747	20	2019-07-01 00:44:00	2019-07-01 01:04:00	3045	34.028511	-118.256668	4275	34.012520	-118.285896	6016	1	One Way	Walk-up	standard	0	July	0	2019-07-01	00:44:00	1
124660227	27	2019-07-01 00:44:00	2019-07-01 01:11:00	3035	34.048401	-118.260948	3049	34.056969	-118.253593	5867	30	One Way	Monthly Pass	standard	0	July	0	2019-07-01	00:44:00	1

Assignment Details¶

Table of Contents

Overview of Python Libraries used and Imports¶

Task1¶

Data Understanding¶

Data Overview and Description¶

Data Preprocessing¶

Set Index¶

Data Cleaning¶

Data Summary¶

Data Info¶

Distributions¶

Value Counts¶

Data Reduction and Transformation¶

Data Transformation¶

Data Reduction¶

Statistical Tests¶

Task2¶

Data Understanding¶

Data Overview and Description¶

Performing PCA¶

Clustering¶

K-Means¶

Gaussian Mixed Modelling¶

DBSCAN¶

Compare Methods¶

Task3¶

Data Understanding¶

Data Overview and Description¶

Visualisation¶

Statistical Analysis¶

Properties¶

Statistics¶

Degree Centrality¶

Degree Distribution¶

Clustering Coefficient¶

Betweenness Centrality¶

Assortativity¶

Resources¶

Column	Description
trip_id	Locally unique integer that identifies the trip.
duration	Length of trip in minutes.
start_time	The date/time when the trip began, presented in ISO 8601 format in local time.
end_time	The date/time when the trip ended, presented in ISO 8601 format in local time.
start_station	The station ID where the trip originated (for station name and more information on each station see the Station Table).
start_lat	The latitude of the station where the trip originated.
start_lon	The longitude of the station where the trip originated.
end_station	The station ID where the trip terminated (for station name and more information on each station see the Station Table).
end_lat	The latitude of the station where the trip terminated.
end_lon	The longitude of the station where the trip terminated.
bike_id	Locally unique integer that identifies the bike.
plan_duration	The number of days that the plan the passholder is using entitles them to ride; 0 is used for a single ride plan (Walk-up).
trip_route_category	"Round Trip" for trips starting and ending at the same station or "One Way" for all other trips.
passholder_type	The name of the passholder's plan.
bike_type	The kind of bike used on the trip, including standard pedalpowered bikes, electric assist bikes, or smart bikes.

Column	Description
area	A, the area of the seed.
perimter	P, the length of the perimeter of the seed.
compactness	A measure of the area of the seed relative to the perimeter,(4πA/P2)
length	The length of the seed.
width	The width of the seed.
asymmetry	A measure of the asymmetry of the seed.
groove_length	The length of the groove in the seed.

	area	perimeter	compactness	length	width	asymmetry	groove_length
0	15.26	14.84	0.871	5.763	3.312	2.221	5.220
1	14.88	14.57	0.881	5.554	3.333	1.018	4.956
2	14.29	14.09	0.905	5.291	3.337	2.699	4.825
3	13.84	13.94	0.895	5.324	3.379	2.259	4.805
4	16.14	14.99	0.903	5.658	3.562	1.355	5.175

	area	perimeter	compactness	length	width	asymmetry	groove_length
count	210.000000	210.000000	210.000000	210.000000	210.000000	210.000000	210.000000
mean	14.847524	14.559286	0.871000	5.628533	3.258605	3.700200	5.408071
std	2.909699	1.305959	0.023594	0.443063	0.377714	1.503559	0.491480
min	10.590000	12.410000	0.808000	4.899000	2.630000	0.765000	4.519000
25%	12.270000	13.450000	0.857250	5.262250	2.944000	2.561500	5.045000
50%	14.355000	14.320000	0.873500	5.523500	3.237000	3.599000	5.223000
75%	17.305000	15.715000	0.887750	5.979750	3.561750	4.768750	5.877000
max	21.180000	17.250000	0.918000	6.675000	4.033000	8.456000	6.550000

	nodes	edges
count	2981.000000	2981.000000
mean	970.580342	1458.960751
std	776.901860	839.483888
min	1.000000	2.000000
25%	288.000000	720.000000
50%	603.000000	1460.000000
75%	1525.000000	2202.000000
max	2699.000000	2888.000000

Property	Description
Degree	The degree of a node in a network is just the number of edges the node has connected to it. `nx.degree(g,n)` will return the degree of node n.
Connected components	The separate components that make up the network. A component is a set of nodes from which it is possible to reach all other nodes in the set. `nx.number_connected_components(g)` returns the number of connected components in the graph.
Diameter	The largest possible number of edges that must be traversed to travel on the shortest path between two nodes in the network. `nx.diameter(g)` will return the diameter of graph `g`.
Density	The density of a graph is a measure of how many edges it has relative to the total number of possible edges it could have. `nx.density(g)` will return the density of graph `g`.
Shortest path	The shortest route along edges in the graph from one node to another. If edges are weighted, the edge weight can be counted as the length of the edge. `nx.shortest_path(g, n1, n2)` will return the shortest path between nodes `n1` and `n2`. `nx.shortest_path(g)` returns the shortest path for each edge.